The study on the anomalous magnetic moment of baryons, i.e., proton and neutron has been for many years [1]}.
Such anomalous magnetic moment of nucleon has been taken into account using the modified 'weak' field expansion of
the fermion propagator having non-trivial correction terms for charged as well as for neutral particles.
The DSE approach has been employed in Refs. [2]}, [3]}to calculate and predict
the nucleon's electromagnetic form factors and parton distribution functions, namely, the rainbow-ladder truncation of QCD's DSE,
which accounts for the momentum dependence of propagators generated by gluon exchange.
Furthermore, the constituent quark model has pointed out that the magnetic moment of proton is the vector sum
of the magnetic moments of its three constituent quarks \(\mu =\mu _{1}+\mu _{2}+\mu _{3}\)  [4]}
(where the sub index \(1,2,3\)  are corresponding to the \(u,d,s\)  quarks).
In this work, we introduce the properties of magnetic moment of nucleon in strong magnetic fields at zero temperature.
To estimate these properties, we follow the idea on the constituent quark model [4]}. Here is
\(\mu _{p} &=& \kappa _{3}\left[\frac{4}{3}\mu _{u}-\frac{1}{3}\mu _{d}\right] =\kappa _{3}\left[\frac{4}{3}\langle \sigma ^{12}\rangle _{u}-\frac{1}{3}\langle \sigma ^{12}\rangle _{d}\right],~\nonumber \\\mu _{n} &=& \kappa _{3}\left[\frac{4}{3}\mu _{d}-\frac{1}{3}\mu _{u}\right] =\kappa _{3}\left[\frac{4}{3}\langle \sigma ^{12}\rangle _{d}-\frac{1}{3}\langle \sigma ^{12}\rangle _{u}\right].\) 
